The shape of the lesson
By the end of the lesson, learners can
- Two slits, many fringes: Change the slit separation, the wavelength and the screen distance and watch the fringe pattern respond exactly as λ = ax / D predicts.
- Bright and dark: Path difference decides what you see.
- Measuring a wavelength: The double slit turns a length measurement into a wavelength.
- Coherent: constant phase, same frequency.
- Bright: path difference nλ.
- Fringes: λ = ax / D.
One picture every idea returns to
Interference is the superposition of waves from two coherent sources (constant phase difference, same frequency). Constructive interference (bright) occurs where the path difference is a whole number of wavelengths; destructive (dark) where it is an odd number of half wavelengths. For Young double-slit fringes, λ = ax / D, where a is the slit separation, x the fringe spacing and D the distance to the screen.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Light plus light makes dark.. Where two coherent waves overlap, they reinforce in some places and cancel in others, painting bright and dark fringes. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Two slits, many fringes | Change the slit separation, the wavelength and the screen distance and watch the fringe pattern respond exactly as λ = ax / D predicts. Project tab 2 of the lab (Interference) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Bright and dark | Path difference decides what you see. | Pairs |
| 21 to 30 min | Teach and check: Measuring a wavelength | The double slit turns a length measurement into a wavelength. | Jigsaw |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 14 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Measuring a wavelength, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Jigsaw
Split the content into expert pieces. Expert groups master one piece each, then regroup so every home team has one expert per piece, and each expert teaches their piece to the team.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The two sources must be coherent; two ordinary lamps will not interfere because their phase difference is random. | In λ = ax / D, a is the slit separation and x the fringe spacing; swapping them inverts the answer. Constructive interference needs a whole number of wavelengths of path difference, while destructive needs an odd number of half wavelengths. |
Interference: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
State the condition for two sources to be coherent.
State, in terms of path difference, the conditions for a bright fringe and for a dark fringe.
In a double-slit experiment the slit separation is 0.40 mm, the screen is 1.5 m away, and the light has a wavelength of 6.3 × 10⁻⁷ m. Find the fringe spacing.
In a double-slit experiment the slit separation is 0.25 mm, the fringe spacing is 2.0 mm and the screen is 0.80 m away. Find the wavelength.
Explain why two separate filament lamps placed side by side do not produce an observable interference pattern.
State two changes that would each increase the fringe spacing in a double-slit experiment.
Answer key and marking notes
- They must have the same frequency ✓
- and a constant phase difference ✓
- Bright (constructive): path difference = a whole number of wavelengths, nλ ✓
- Dark (destructive): path difference = an odd number of half wavelengths, (n + ½)λ ✓
- x = λD / a = (6.3 × 10⁻⁷ × 1.5) / (0.40 × 10⁻³) ✓
- x = 2.4 × 10⁻³ m = 2.4 mm ✓
- λ = ax / D = (0.25 × 10⁻³ × 2.0 × 10⁻³) / 0.80 ✓
- λ = 6.3 × 10⁻⁷ m ✓
- They are not coherent: each emits light with a randomly changing phase ✓
- so the phase difference between them varies rapidly and no steady pattern of fringes forms ✓
- Move the screen further away (increase D) ✓
- Reduce the slit separation a (or use a longer wavelength) ✓
12 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Two sources are coherent if they have a constant phase difference and the same:
- Afrequency
- Bamplitude
- Cdirection
- Dspeed only
A bright fringe forms where the path difference is:
- Aan odd number of half wavelengths
- Ba quarter wavelength
- Ca whole number of wavelengths
- Dalways zero
The double-slit fringe spacing is given by:
- Ax = λa/D
- Bx = λD/a
- Cx = aD/λ
- Dx = a/(λD)
Slit separation 0.50 mm, screen 2.0 m, λ = 600 nm. The fringe spacing is:
- A0.42 mm
- B1.2 mm
- C4.8 mm
- D2.4 mm
A dark fringe forms where the path difference is:
- Aan odd number of half wavelengths
- Ba whole number of wavelengths
- Czero only
- Done wavelength
In a double-slit setup, a = 0.20 mm, x = 3.0 mm, D = 1.0 m. The wavelength is:
- A1.5 × 10⁻⁷ m
- B6.0 × 10⁻⁶ m
- C6.0 × 10⁻⁷ m
- D6.7 × 10⁻⁸ m
Two separate lamps do not produce interference fringes because they are:
- Atoo bright
- Bnot coherent
- Cthe same colour
- Dtoo far apart
To widen the fringes you could:
- Aincrease the slit separation
- Buse a higher frequency
- Cuse a shorter wavelength
- Dincrease the distance to the screen
At a point the path difference is 2.0 wavelengths. The point is:
- Abright
- Bdark
- Chalf bright
- Dunaffected
Increasing the slit separation a, with everything else fixed, makes the fringes:
- Afurther apart
- Bunchanged
- Ccloser together
- Ddisappear
Red light gives wider fringes than blue light in the same apparatus because red light has a:
- Ahigher frequency
- Blonger wavelength
- Cgreater speed
- Dlarger amplitude
The central fringe of a double-slit pattern is:
- Adark
- Bcoloured
- Cabsent
- Dbright (zero path difference)
Quiz key
Coherent sources share frequency and a fixed phase relation.
Constructive interference needs path difference nλ.
x = λD/a.
x = λD/a = (6.0 × 10⁻⁷ × 2.0)/(5.0 × 10⁻⁴) = 2.4 mm.
Destructive interference needs (n + ½)λ.
λ = ax/D = (2.0 × 10⁻⁴)(3.0 × 10⁻³)/1.0 = 6.0 × 10⁻⁷ m.
Their phase difference varies randomly, so no steady pattern forms.
x = λD/a increases with D.
A whole number of wavelengths gives constructive interference (bright).
x = λD/a decreases as a increases.
x ∝ λ, and red has the longer wavelength.
Zero path difference gives constructive interference, a bright central fringe.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.